Topics
5. Surface Area and Volume
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AustraliaNSW
Year 11

5.065 Volume of composite solids

Lesson
Worksheet
Practice
Lesson

 

Volume of composite solids

Composite solids are just a combination of simpler solids.  

To find the volume of composite solids such as these:

Strategy 1

  • Break down the shape into smaller and simpler solids
  • Find the volume of the individual smaller solids to be either added or subtracted
  • Add or subtract the volumes of the individual solids as necessary to find the total volume

Strategy 2

  • If the solid forms a prism, we could always shortcut the process by calculating the area of the end and multiplying by the height/length of the prism

Our aim is to choose a method we feel most comfortable with.

 

Practice questions

Question 1

Question 2

Find the volume of the figure shown, correct to two decimal places.

A three-dimensional composite figure which is a combination of a rectangular prism and a half-cylinder. The length of the rectangular prism  is labeled as $10$10 m. The base of the rectangular prism has congruent sides as indicated by the single tick mark on each side, with the bottom side labeled $4$4 m.  The flat surface of the half cylinder coincides with the top face of the rectangular prism such that its height directly overlaps the rectangle's length. The diameter of the semicircular base of the cylinder is the top side of the base of the rectangular prism. 

Outcomes

MS11-4

performs calculations in relation to two-dimensional and three-dimensional figures

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